Radial basis function nets

The popular radial basis function nets (RBF nets) model nonlinear relationships by linear combinations of basis functions (Zell [1994] Jagemann [1998] Zupan and Gasteiger [1993]). Functions are called to be radial when their values, starting from a central point, monotonously ascend or descend such as the Cauchy function or the modified Gauss function at Eq. (6.125) ... 

Chen, S., Cowan, C. F. N., and Grant, P. M., Orthogonal least squares learning algorithm for radial basis function networks, IEEE Trans. Neur. Net. 2(2), 302-309 (1991). 

We view the real or the simulated system as a black box that transforms inputs into outputs. Experiments with such a system are often analyzed through an approximating regression or analysis of variance model. Other types of approximating models include those for Kriging, neural nets, radial basis functions, and various types of splines. We call such approximating models metamodels other names include auxiliary models, emulators, and response surfaces. The simulation itself is a model of some real-world system. The goal is to build a parsimonious metamodel that describes the input-output relationship in simple terms. 

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